Examples of -Skew -Armendariz Rings

Abstract

In this paper extensive examples and related counterexamples of the category of -skew -Armendariz rings are given. This category of rings regards a new generalization for the concepts of -skew Armendariz and skew -Armendariz rings. A ring is called -skew -Armendariz if for any ( ) Σ and ( ) Σ such that ( ) ( ) ( ), then ( ) ( ) for each and . First some general properties of -skew -Armendariz rings are studied and then relations between -skew -Armendariz rings and other related rings are investigated. Also various examples of non -skew -Armendariz rings are established.